17M.1.SL.TZ1.S_7

pestleMathematicsAISLPaper 117M· sl-1-3-geometric-sequences-and-seriessource ↗

The first three terms of a geometric sequence are $\ln {x^{16}}$ , $\ln {x^8}$ , $\ln {x^4}$ , for $x > 0$ .

Find the common ratio.

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

correct use $\log {x^n} = n\log x$ A1

eg $\,\,\,\,\,$ $16\ln x$

valid approach to find $r$ (M1)

eg $\,\,\,\,\,$ $\frac{{{u_{n + 1}}}}{{{u_n}}},{\text{ }}\frac{{\ln {x^8}}}{{\ln {x^{16}}}},{\text{ }}\frac{{4\ln x}}{{8\ln x}},{\text{ }}\ln {x^4} = \ln {x^{16}} \times {r^2}$

$r = \frac{1}{2}$ A1 N2

[3 marks]

Examiners’ report

[N/A]